Effective narrow ladder model for two quantum wires on a semiconducting substrate

TL;DR

This paper develops a narrow ladder model to study two quantum wires on a semiconducting substrate, revealing how substrate-mediated interactions influence their correlated electronic phases, including Mott insulators and Luttinger liquids.

Contribution

It introduces a narrow ladder model approach for coupled quantum wires on substrates, enabling analysis of substrate-mediated interactions and their effects on electronic phases.

Findings

Substrate can mediate effective wire-wire coupling.

Wires can form a Mott charge-density-wave insulator.

Luttinger liquid phase can be stabilized under certain conditions.

Abstract

We present a theoretical study of two spinless fermion wires coupled to a three dimensional semiconducting substrate. We develop a mapping of wires and substrate onto a system of two coupled two-dimensional ladder lattices using a block Lanczos algorithm. We then approximate the resulting system by narrow ladder models, which can be investigated using the density-matrix renormalization group method. In the absence of any direct wire-wire hopping we find that the substrate can mediate an effective wire-wire coupling so that the wires could form an effective two-leg ladder with a Mott charge-density-wave insulating ground state for arbitrarily small nearest-neighbor repulsion. In other cases the wires remain effectively uncoupled even for strong wire-substrate hybridizations leading to the possible stabilization of the Luttinger liquid phase at finite nearest-neighbor repulsion as found previously for single wires on substrates. These investigations show that it may be difficult to determine under which conditions the physics of correlated one-dimensional electrons can be realized in arrays of atomic wires on semiconducting substrates because they seem to depend on the model (and consequently material) particulars.